Show that any positive odd integer is of the form 4q+1 or 4q+3, where q is some integer.

Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q + 1, where q is some integer.

Use division algorithm to show that any positive odd integer is of the form 6q + 1, or 6q + 3 or 6q + 5, where q is some integer

The square of an odd integer is of the form 4q + r where r is :

Show that the square of any positive integer of the form 3m or 3m + 1 for some integer n.

Use division algorithm to show that the cube of any positive integer is of the form 9 m, 9m + 1 or 9m + 8.

Show that 107 is of the form 4q+3 for any integer q.